It shouldn't hinder much (the CPU Cooler will hinder more than GPU), but I personally recommend getting HIS' HD 7770 "iCooler", not Sapphire's HD 7770s.
HIS' HD 7770s are the best 7770s you can get on the market right now: they are small, very energy efficient (consume less energy out of all other HD 7770s), very cool and quiet, while performing roughly the same (and even better, in some cases). There are HIS HD 7770 "iCooler", and HIS HD 7770 "IceQ X". I personally highly recommend getting "iCooler" one.
Sapphire's cards are very good at "medium" and "high" pricing segments, but at "low" and "tight budget" pricing segments HIS completely dominates the market with it's "iCooler".
Also, you'll probably wouldn't need to do that, but I'll suggest anyway that you change that PSU for something better:
"CX"es are the worst of what Corsair offers on the market right now, they can work for ultra-cheap (like, "HTPC cheap") setups, but you'd better not use them in desktops, because they are basically an outsourced product assembled of the cheapest components possible and they can be quite unreliable.
What I'm suggesting is that you get a 450~500W PSU, and if Corsair, then at least "TX" line - they are MUCH better.
ya I have a iceQ they are Decent but my psu has not gave me any problems for a year it had a Him to it for a while but that is gone now its running like a Champ Ill keep that in mind I'm thinking of the Seasonic 520 for 64 bucks its 20 dollars off atm but can't get that for another 2 weeks
Yeah, SeaSonic would do just fine (since, basically, 60% of all Corsair's high-quality PSUs are made by SeaSonic, lol. Starting from "TX"es and up to expensive beasts like AX "1200i").
As for GPU: HD 7750 is so much weaker than HD 7770, than even the weakest GTX 550 Ti (THE most weakest modern Nvidia's GPU up to date) will kick it's ass easily. So better not. :\
Just get that "HD 7770 iCooler" and you'll be absolutely fine. Don't try to economize by jumping lower, man. Usually nothing good comes out of that. 7770 is the lowest you should get.
You will be actually surprised by how good HIS' "HD 7770 iCooler" performs for such a cheap, low-level GPU. There's a vastly big difference between previous gen and current gen.
Simply because they moved to a new tech-process even the lowest of GPUs started performing like "low-mid/mid" level cards. Just don't forget to always download freshest drivers.
You would be able to AA some "2~3 years old" games just fine, and even some of the most freshest ones (well, maybe just with exception of such MONSTERS as "Max Payne 3", "Far Cry 3", or "Crysis 3"), and you'll probably would be able to max out almost anything that's "4 years old" and older (like, for example, "Dragon Age Origins", "Mass Effect", or GTA IV).
Zalman's Coolers suck major balls. Don't even think of getting them unless it's "CNPS12X" (this is the ONLY really worthwhile Cooler Zalman made, so far).
My point is in that Hyper 212 had tons of different versions/revisions through the years, and some of them are bigger than others, so if for some it might work, for other it might not.
It all depends on what particular version of Hyper 212 you're getting.
Yep I'm going be buying a few Startech fan power splitter cables So I can have a fan in the front of my case in for the Cooler it self Not sure how many I need I only have 3 fans atm 2 on top pushing Air out the case in one for the cpu I'm going add one to the front of my case also.